Question

Help!! Which of the following best represents Z1 • Z2 select all that apply

Answer 1

$z_1=\sqrt{3}\left(cos\:\frac{\pi }{4}+i\:sin\:\frac{\pi }{4}\right)$

$z_2=\sqrt{6}\left(cos\:\frac{3\pi \:}{4}+i\:sin\:\frac{3\pi \:}{4}\right)$

$\cos \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}$

$\sin \left(\frac{\pi }{4}\right)=\frac{\sqrt{2}}{2}$

$\cos \left(\frac{3\pi }{4}\right)=-\frac{\sqrt{2}}{2}$

$\sin \left(\frac{3\pi }{4}\right)=\frac{\sqrt{2}}{2}$

$Z_1*Z_2=\sqrt{3}\left(cos\:\frac{\pi }{4}+i\:sin\:\frac{\pi }{4}\right)\cdot \sqrt{6}\left(cos\:\frac{3\pi \:}{4}+i\:sin\:\frac{3\pi \:}{4}\right)$

$=\sqrt{3}\left(\frac{\sqrt{2}}{2}+\:i\frac{\sqrt{2}}{2}\right)\cdot \sqrt{6}\left(\frac{-\sqrt{2}}{2}+\:i\frac{\sqrt{2}}{2}\right)$

On simplifying, we get

$Z_1* Z_2 =-3\sqrt{2}$

Therefore, correct option is  1st option.